So we know that atoms can transform from one element into another by the natural process of radioactivity. Certain isotopes of certain elements are unstable because there are either too many or not enough neutrons in the nucleus to stabilise the electric repulsion of the positively charged protons. If there are too many protons, the nucleus can eject a bundle of two protons and two neutrons (known as an alpha particle and actually the same thing as the nucleus of a helium atom), and reduce its atomic number by two. If there are too many neutrons, a neutron can decay into a proton plus an electron and the electron ends up being ejected at high energy (such electrons being known as beta particles). This beta decay increases the atomic number of the nucleus by one.

There are other processes that can transform atoms by rearranging the numbers of protons and neutrons in the nuclei. A large atom can split apart into two smaller atoms, also ejecting some of the excess neutrons during the reaction. A few isotopes of heavy elements can undergo this process as a form of natural radioactive decay. Our old friends uranium-235 and uranium-238 both decay in this way a small fraction of the time (less than one in a million decays) rather than by alpha decay. The products can be various atoms such as caesium, zirconium, iodine, molybdenum, zinc, and so on.[1] This form of radioactive decay is called spontaneous fission.

Fission can also occur in another way. If a heavy nucleus is struck by a smaller particle, the collision can crack the nucleus apart. Neutrons are the best impacting particle, since they are very common, relatively heavy as sub-atomic particles go, and electrically neutral, which means they aren't repelled by the positively charged nucleus as an incoming proton would be.

When a neutron of roughly the right kinetic energy hits a nucleus of a heavy atom, such as uranium or plutonium, the nucleus splits into two smaller atoms. As mentioned above it also spits out some new neutrons, three in the case of the isotope uranium-235 (the impacting neutron is absorbed and three new neutrons are released, so there are two more going out than coming in). The interesting thing is that these neutrons generated by the fission reaction have the right energy to split apart other uranium-235 atoms if they happen to hit any. And if that happens, the three atoms split will emit three more neutrons each. They can split nine more uranium atoms, generating 27 more neutrons. And so on.

A small lump of uranium contains trillions upon trillions of atoms. A piece the size of a pea contains about 1020 atoms. If an energetic neutron hits that piece of uranium, it can start a chain reaction that very quickly splits apart every uranium-235 nucleus.

Now here's the thing. A uranium-235 nucleus might split, for example, into rubidium-90 plus caesium-143. But a uranium-235 nucleus contains more mass than a nucleus of rubidium-90 plus a nucleus of caesium-143 plus two extra neutrons. Even though the uranium-235 nucleus contains 92 protons and 143 neutrons, and the total numbers of protons and neutrons after the reaction are the same. The numbers of each particle are conserved, but the mass is not. What's going on here?

The answer has to do with that little equation devised by Albert Einstein: E = mc2. The nuclei of atoms are held together against the electromagnetic force trying to repel all the protons from one another by a different force, called the strong nuclear force. To do this, the electrical potential energy inherent in the mass of tightly packed protons must be overpowered by the energy of the strong nuclear force. The result is that the total potential energy of an atomic nucleus is actually lower than that of a bunch of protons so far apart that they feel vanishingly small electrical repulsion. And when the total energy is lower, the mass is lower, because of the equivalence of mass and energy represented in Einstein's equation.

So each atomic nucleus (more complicated than that of hydrogen-1 with just a lone proton) actually contains less mass than the total mass of the individual protons and neutrons that make it up. What's more, the size of this difference, or mass defect, depends on the size of the nucleus in a slightly complicated way. Small nuclei experience a small amount of strong nuclear force, so they are held together relatively weakly. As the nuclei grow larger, the strong force holding the protons and neutrons together grows. This is similar to how small objects can be pulled apart fairly easily, but objects the size of Earth cannot because the gravitational force holding it together is so much bigger. So larger nuclei are held together more strongly, and the size of the mass defect per particle grows.

But then things get more complicated. The strong nuclear force is not like gravity or electromagnetism at all. Gravity has an unlimited range. It falls off moderately quickly with distance, but our sun still has a significant gravitational effect on Earth, the other planets, and even on nearby stars. The nuclear force is very strong at extreme close range, but drops to zero just a short distance further out. It's more like Velcro. Get two objects within a millimetre or so of each other, and Velcro will hold them together strongly. But at five millimetres range, Velcro is absolutely powerless. The strong nuclear force happens to fall off to zero once the nucleons (protons or neutrons) get about as far apart as the size of half a dozen nucleons. Now imagine the nucleus of a large atom. It's a ball made of protons and neutrons stuck together by the strong force. If that ball is big enough the nucleons on one side of it will be far enough away from the nucleons on the other side that they won't feel the strong force from them. So as the nuclei get bigger and bigger, the overall binding effect of the strong force, per nucleon, starts becoming weaker again.

There's a turnover point where the mass defect per nucleon is the greatest, and that happens to occur for the atom we know as nickel-62, with 28 protons and 34 neutrons. Nickel-62 is actually a fairly rare isotope of nickel, making up about 3.6% of naturally occurring nickel - the most common isotope is nickel-58. The mass-defect-per-nucleon curve is very flat around mass number 62, and two isotopes of iron also have mass defects per nucleon of almost the same amount as nickel-62. These are iron-58 and iron-56. Of these three isotopes, iron-56 is by far the most common, making up almost 92% of all the iron found in nature.[2]

These three nuclei, nickel-62, iron-58, and iron-56, are the most energetically stable of all isotopes. Elements with greater mass numbers than this 56 to 62 range have a lower mass defect per nucleon, i.e. they have a greater total mass per nucleon than these isotopes. So when they split apart in a fission reaction, the resulting smaller product atoms tend to have a greater total mass defect, i.e. their total mass is now lower. In other words, the mass of the atom going into the reaction is greater than the mass of the products. And where does the mass go? Well, it gets turned into energy according to E = mc2, giving large amounts of kinetic energy to the reaction products. Produce enough fission reactions and this released energy quickly heats up the material the atom is in to a high temperature. This energy, produced by the mass deficit of the strong nuclear force, is called the nuclear binding energy, and can be thought of as the amount of energy that is holding the nucleus together.

So, if we take our lump of uranium-235 and fire a neutron at it, it splits an atom and releases three new neutrons plus quite a lot of energy. The new neutrons can split more atoms in the cascade described above, and each atom releases more energy. The result, if this reaction continues cascading uncontrollably like this, is a nuclear meltdown in which the lump of uranium rapidly melts - or, if it can't melt and flow away from itself fast enough, a nuclear explosion. This is the essential principle of a nuclear bomb. There are details in how you trigger the reaction and how you make the bomb safe before you trigger it, but they're not important right now (and would probably get me stuck on some sort of intelligence watch list if I talked any more about them).

On the other hand, if you can control the number of energetic neutrons somehow so they don't get out of hand, and siphon off the generated energy fast enough, you can produce a nuclear reaction that can serve as the basis for power generation. This can be achieved by putting the reacting material in close proximity to some material that absorbs neutrons. Graphite and water are good materials, and both are used in nuclear reactors of various designs. By moving these materials suitably, you can control the number of neutrons and turn the reaction up or down or off altogether. And this is basically how nuclear power plants work. A good nuclear power plant design will have enormous numbers of safety interlocks and failsafes to ensure the reaction can't get out of control, but there can still be unforeseen risks, alas.

This nuclear fission, the breaking apart of heavy nuclei, is only one way to generate energy from nuclear reactions. Remember that the mass defect per nucleon is highest for mass numbers around 60. This means that if you take two atoms with fewer protons than iron, and combine them to form a single heavier atom, you can also release energy. This process is called nuclear fusion, and is a very different beast to nuclear fission.

The biggest bang for your buck from fusion comes from fusing together the very lightest atoms of all, hydrogen. If you can manage to get two protons (hydrogen nuclei) and two neutrons together, they will fuse into a helium nucleus. The helium nucleus has a significantly lower mass than the four individual particles, and the remainder is converted into energy and released. The trouble is it's extremely difficult to get four particles like that close enough together all at once for the strong nuclear force to start working on them.

An easier road comes if you take two atoms of the isotope hydrogen-2, each of which has a nucleus consisting of one proton and one neutron. Hydrogen-2 is also known by the name deuterium, and it occurs naturally on Earth at a rate of about 0.016% of all hydrogen atoms. If you mash just two of these nuclei together, they can fuse into a helium nucleus, releasing energy as they do so. The most ready source of deuterium we have is actually in plain old water. 0.016% of the water molecules contain an atom of deuterium instead of regular hydrogen. Such water molecules are called heavy water and can be separated and concentrated by a fairly simple process.

So theoretically we can release huge amounts of energy from water by fusing the deuterium into helium. There are also other possible fusion reactions, for example involving hydrogen-3, or tritium. The good thing about nuclear fusion is that it poses none of the risks of nuclear fission. We don't have to mine expensive uranium ores from the ground. We don't have to be careful about controlling the reaction lest it turn into a bomb, since it doesn't work on the same neutron chain reaction as fission - if something goes wrong, the reaction just stops. And it doesn't produce dangerously radioactive waste products like rubidium-90 and caesium-143 and other scary isotopes (it actually makes helium, which is a scarce natural resource that we could use more of!).[3] The main problem with nuclear fusion is we don't have the technology to do it yet, at least in a way that generates a reaction that produces more energy than we have to put in to get the fusion started.

That lies in the future, but it's a future worth pursuing. Nuclear fusion, if we can get it to work here on Earth, could potentially solve the major problems we face with our energy supplies at the moment - mostly the fact that most of the energy we use currently comes from sources that are dangerous to the short and/or long term health of our own civilisation.

[1] Any particular fission reaction can produce a range of possible product isotopes. For a full list, and the various probabilities of producing each of the different product isotopes, see this Wikipedia page on fission product yield.

[2] And we will meet iron-56 again later on. It's a very important isotope in the cosmic scheme of things.

[3] Some fusion reactions produce very high energy neutrons, which can hit material around the reaction and convert atoms into radioactive isotopes. So there is potential there to produce dangerous waste products, but this can be avoided with judicious reactor design.